What happens if one can't sleep at a sleep study. do they allow to bring meds or mouthguards?

They would : Explain and discuss everything with you. Sometimes they can do a split study - part without a snore guard and part with. Depends on the facility and their protocol. Also a typical night guard is not a snoring / sleep apnea device. Hope this helps.

Yes: You can take a sleeping aid as it doesnt affect the things that they observe during your sleep.

Yes: Yes but they may consider a home sleep study- not as effective in terms of the info provided, but a viable alternative.